Control systems are used to move a variety of control objects from an initial position to a final position. For example, data storage devices commonly utilize a closed loop servo control system to position a data transducer adjacent individual tracks on a data storage medium.
A well known servo control approach is Pontryagin's Time-Optimal Control Solution, which generally operates to change the system state in minimum time while at all times using all available system power. This approach is sometimes also referred to as Bang-Bang Control.
While time-optimal, some real world applications can limit the viability of this approach due to the presence of variable or unquantifiable system resonances. More particularly, abrupt changes in jerk (change in acceleration with respect to time) can serve as a broad spectrum excitation of the system, resulting in unacceptably long settle times at the final position.
Accordingly, there is a continual need for improvements in the manner in which control trajectories are formulated as part of a control solution, such as but not limited to the controlled movement of a transducer in a data storage device.